6-6 Systems of Linear Inequalities Learning Targets: I can solve systems of linear inequalities by graphing. I can model real-world situations using systems of linear inequalities.

System of Linear Inequalities: made up of two or more linear inequalities Solution of a system of linear inequalities: an ordered pair that makes all the inequalities in the system true Learning Targets: I can solve systems of linear inequalities by graphing. I can model real-world situations using systems of linear inequalities.

Problem 1: Graphing a System of Linear Inequalities Determine whether the ordered pair is a solution of the given system 1−𝑥≥3𝑦 3𝑦−1>2𝑥 (0,1) Learning Targets: I can solve systems of linear inequalities by graphing.

Determine whether the ordered pair is a solution of the given system 2𝑥+3𝑦>2 3𝑥+5𝑦>1 (−2,3) Learning Targets: I can solve systems of linear inequalities by graphing.

Problem 1: Graphing a System of Linear Inequalities Learning Targets: I can solve systems of linear inequalities by graphing.

Learning Targets: I can solve systems of linear inequalities by graphing.

Learning Targets: I can solve systems of linear inequalities by graphing.

Problem 2: Writing a System of Inequalities From a Graph What systems of inequalities is represented by the graph below? Learning Targets: I can solve systems of linear inequalities by graphing.

What systems of inequalities is represented by the graph below? Learning Targets: I can solve systems of linear inequalities by graphing.

What systems of inequalities is represented by the graph below? Learning Targets: I can solve systems of linear inequalities by graphing.

Problem 3: Using a System of Inequalities You are planning what to do after school. You can spend at most 6 hours playing basketball and doing homework. You want to spend less than 2 hours playing basketball. You must spend at least 1.5 hours on homework. What is a graph showing how you can spend your time? Learning Targets: I can solve systems of linear inequalities by graphing. I can model real-world situations using systems of linear inequalities.

Problem 3: Using a System of Inequalities A dog walker earns $15 per hour. She also earns $12 per hour for babysitting. She wants to earn at least $300 next week, but can work no more that 30 hours. What is a graph showing how many hours she can work at each job? Learning Targets: I can solve systems of linear inequalities by graphing. I can model real-world situations using systems of linear inequalities.